At first he attended the Kunstgewerbeschule (school of applied arts) in Vienna, from 1906 to 1910 he studied at the Akademie der bildenden Künste (academy of fine arts) in Vienna, where Christian Griepenkerl and Rudolf Bacher were his teachers. In 1919, after the end of World War I, he became a member of the Secession and began working as a freelance artist.

In 1955, Dobrowsky was admitted to the Secession as a honortary member. He was honoured with several important state awards at a quite early time of his career. From 1946 to 1963, he was a professor of painting at the Vienna Academy, during which time he influenced subsequent generations of artists. Important artists such as Alfred Hrdlicka, Josef Mikl and Wolfgang Hollegha were among his students.

Dobrowsky died on January 9th 1964 in Tullnerbach where he had lived since 1959. His work is considered to be a pillar of the development of modern painting in Austria – it is presented in numerous museums and private collections.